Two-photon Jaynes-Cummings systems interacting with a classical field

If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.